A124377 Riordan array (1/(1-x-x^2),x/(1+x)).

1, 1, 1, 2, 0, 1, 3, 2, -1, 1, 5, 1, 3, -2, 1, 8, 4, -2, 5, -3, 1, 13, 4, 6, -7, 8, -4, 1, 21, 9, -2, 13, -15, 12, -5, 1, 34, 12, 11, -15, 28, -27, 17, -6, 1, 55, 22, 1, 26, -43, 55, -44, 23, -7, 1, 89, 33, 21

Offset: 0

Author

Paul Barry, Oct 29 2006

Keywords

• easy
• sign
• tabl

Comments

First column is F(n+1). Second column is A008346. Row sums are F(n+2). Diagonal sums are A094966(n+1). Product of A007318 and A124377 is the Riordan array ((1-x)/(1-3x+x^2),x), the sequence array for F(2n+1).

Examples

			Triangle begins
1,
1, 1,
2, 0, 1,
3, 2, -1, 1,
5, 1, 3, -2, 1,
8, 4, -2, 5, -3, 1,
13, 4, 6, -7, 8, -4, 1,
21, 9, -2, 13, -15, 12, -5, 1
		

Crossrefs

Cf. A000045

Formula

Number triangle T(n,k)=sum{j=0..n-k, C(j-k,n-k-j)}*[k<=n]

T(n,k)=T(n-1,k-1)+2*T(n-2,k)-T(n-2,k-1)+T(n-3,k)-T(n-3,k-1), T(0,0)=T(1,0)=T(1,1)=1, T(n,k)=0 if k<0 or if k>n. - Philippe Deléham, Jan 12 2014

T(n,0)=A000045(n+1), T(n,n)=1, T(n,k)=T(n-1,k-1)-T(n-1,k) for 0Philippe Deléham, Jan 12 2014